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GATE2020 Engg Mechanics Rapid Mini Mock (App update required to attempt this test)

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Question 1

Two weights are supported as shown in the figure. Tension in string PQ is ______.

Question 2

For a linear elastic structural system, minimization of potential energy yields

Question 3

A particle of mass 2 kg is travelling at a velocity of 1.5 m/s. A force f(t)=3t2 (in N) is applied to it in the direction of motion for a duration of 2 seconds, where t denotes time in seconds. The velocity (in m/s, up to one decimal place) of the particle immediately after the removal of
the force is________

Question 4

A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time t, the equation of motion for the free vibration of the system is The natural frequency of the system is

Question 5

Mathematical idealization of a crame has three bars with their vertices arranged as shown in the figure with a laod of 80 kN hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member QR, FQR will be

Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\Civil-Engineering-2014_files\image138.jpg

Question 6

Two rectangular block of weight and connected by a flexible cord resting upon a horizontal plane and an incline are shown in figure. The angle of inclination of the incline plane is 23 at which motion of the system will impend. Find the coefficient of static friction. (Take )

Question 7

A particle moves along a curve whose parametric equations are : x=t3 + 2t, y=-3e-2t and z = 2 sin (5t), where x, y and z show variations of the distance covered by the particle (in cm) with time t (in s). The magnitude of the acceleration of the particle (in cm/s2) at t = 0 is _________ cm2/s

Question 8

A vehicle applies brake and skids through a distance of 60 m, before colliding with another parked vehicle, the weight of which is 75% of former. If distance travelled by both vehicle after collision is 15 m before stopping, then the initial speed (in m/sec) of moving vehicle was
[Assume collision is perfectly plastic, brake efficiency = 100% and coefficient of friction (f) = 0.55]

Question 9

Block A weighing 200 kg resting on the rough floor supports block B weighing 100 kg as shown in the figure. Both the blocks are connected with a rope passing over a smooth pulley. Find the force P required to impending motion. (Take  and coefficient of friction = 0.3)

Question 10

A bullet of weight 1.4g enters a wooden partition block at a velocity of 955 m/s and 0.003s after entering the block. Determine the length penetration of bullet.

Question 11

A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force P acts at C as shown. Let RAh and RBh be the horizontal reactions at supports A and B, respectively, and RAv be the vertical reaction at support A. Self- weight of the member may be ignored.
Which one of the following sets gives the correct magnitudes of and ?

Question 12

A particle P is moving on a circular path of radius 1m. The angular location of the particle is described by =2 sin t. The magnitude of the total acceleration (in m/s2) of the particle at time t=π/3 seconds is_
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